Rotating Fluids in Geophysical and Industrial Applications by E. J. Hopfinger (eds.)
By E. J. Hopfinger (eds.)
The quantity provides a finished evaluate of rotation results on fluid habit, emphasizing non-linear methods. the topic is brought by way of giving a number of examples of rotating fluids encountered in geophysics and engineering. this is often then by means of a dialogue of the proper scales and parameters of rotating circulation, and an advent to geostrophic stability and vorticity innovations. There are few books on rotating fluids and this quantity is, as a result, a great addition. it's the first quantity which includes a unified view of turbulence in rotating fluids, instability and vortex dynamics. a few points of wave motions coated listed here are no longer came across elsewhere.
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Extra resources for Rotating Fluids in Geophysical and Industrial Applications
5), is known as Kelvin 's theorem (14) lt is valid for an inviscid fluid, as long as no extemal force is applied. This theorem is easily demonstrated by expressing in (14) the circulation as the vorticity flux across a surface bounded by the closed line C (eq. 3). The classic result on the variation in time of a flux is then used. One obtains ~ = i\t if. i . i ) ) . i1 ds , (15) combined with equation (8) for vorticity. The final result (14) follows from the fact that the velocity and vorticity fields are non-divergent The conservation of circulation is a very strong constraint imposed on the flow.
Parameters and Scales 25 The energy cascade is an inverse cascade with a scale doubling in a time of about 30 initial turnover time scales. On an f-plane, the presence of end boundaries sets an upper bound to the turbulence scale due to Ekman dissipation. The limiting upper scale LE being determined by the equality of the Ekman spin-down timet and turnover time Lt/u, giving Lt < LE = ut. When the boundaries form a ß-plane, the turbulent energy can be carried away by Rossby waves. The limiting scale Lß, called the Rhines scale, is given by the equality of the turnover time scale Lt/u and the Rossby wave period, giving Lt < Lß = 1t(2u/ß)l/2.
Incompressible, a:xisymmetric, laminar flow Consider the axisymmetric flow around an axis Oz. In the cylindrical coordinate system (0,r,8,z), the velocity components are the radial, azimuthat and axial components, respectively u,v and w. All components depend only on the r and z Coordinates. CAv and r"df (57) It is also common to introduce the circulation C(r,z), which is l/21t the circulation along a circle of radius r centered on the axis C(r,z) = r v(r,z) . (58) Differentiating (53) with respect to z and (55) with respect to r, pressure is eliminated by subtracting the two resulting equations.